We prove that the correlation of a depth-d
unbounded fanin circuit of size S with parity
of n variables is at most 2^{-\Omega(n/(\log S)^{d-1})}.

Substantial revision of main proof.

We prove that the correlation of a depth-d
unbounded fanin circuit of size S with parity
of n variables is at most 2^{-\Omega(n/(\log S)^{d-1})}.